Josefina Casasayas

Invariant manifolds for a class of parabolic points

The authors consider a class of maps having the origin as a parabolic fixed point with a nondiagonalizable linear part, degenerate in the sense that it has a line of fixed points through it, and they give conditions for the existence and regularity of invariant manifolds. This class is motivated from Poincare maps of flows appearing in celestial mechanics.

Central configurations of the planar 1+N body problem

In this paper, we give a new derivation of the equations for the central configurations of the 1+n body problem. In the case of equal masses, we show that forn large enough there exists only one solution. Our lower bound forn improves by several orders of magnitude the one previously found by Hall.

A restricted charged four-body problem

We consider a restricted charged four body problem which reduces to a two degrees of freedom Hamiltonian system, and prove the existence of infinite symmetric periodic orbits with arbitrarily large extremal period. Also, it is shown that an appropriate restriction of a Poincaré map of the system is conjugate to the shift homeomorphism on a certain symbolic alphabet.

Homoclinic orbits to parabolic points

Abstract. We give a proof of the Poincaré-Melnikov method in the case of non-Hamiltonian perturbations of one and a half degrees of freedom Hamiltonians, having orbits homoclinic to degenerate periodic orbits of parabolic type.

Periodic orbits of the integrable swinging Atwood’s machine

We identify all the periodic orbits of the integrable swinging Atwood’s machine by calculating the rotation number of each orbit on its invariant tori in phase space, and also providing explicit formulas for the initial conditions needed to generate each orbit.

Infinity manifold of a swinging Atwood's machine

The unbounded motions of a swinging Atwoods machine are analysed by blowing up the singularity at infinity. The asymptotic motion is reduced to a gradient flow on an ellipsoid. By studying the flow on this ellipsoid it is shown that the unbounded orbits oscillate either an infinite number of times or not at all, depending only on a critical value of the mass ratio.

Unbounded orbits of a swinging Atwood’s machine

The motion of a swinging Atwood’s machine is examined when the orbits are unbounded. Expressions for the asymptotic behavior of the orbits are derived that exhibit either an infinite number of oscillations or no oscillations, depending only on a critical value of the mass ratio.

Qualitative study of motion under the potentials

AbstractThe two-parameter family of hamiltonians systems defined by

A Perturbation of the Relativistic Kepler Problem

H_{(a,\alpha )} (r,\theta ,p_r ,p_\theta ) = (p_r^2 + p_\theta ^2 r^{ - 2} )/2 - ar^{ - \alpha } ,\alpha ,a \in \Re ^ +